Binary data coding, also referred to as simply ‘binary coding,’ is a mapping of a plurality of information bits of a data word into a format that provides an improved result when one or more of storing, processing and transmitting the data word. For example, the Gray code developed and patented by Frank Gray of Bell Labs in 1947 (U.S. Pat. No. 2,632,058) is a binary data code based on a binary numbering system having successive values that differ from one another by a single bit. The Gray code is useful in a variety of applications in which changes from one binary value to another may be misinterpreted or produce errors if an un-coded or ‘straight’ binary representation of data were to be used. For example, Gray codes are used in a wide variety of applications including, but not limited to, error correction (e.g., in digital communication), position encoders (e.g., rotary encoders), digital counters, and even genetic algorithms. Other binary data codes including, but not limited to, various error-correction codes (ECCs), introduce redundancy to enable bit errors to be detected and, in some instances, corrected. ECCs of various forms are used extensively in data communication and data storage in which various random error processes may introduce bit errors in data being one or more of handled, processed, transmitted and stored. In yet other examples, binary codes are used to configure data in a manner that reduces a chance that bit errors may be produced by a system that one or more of handles, processes, transmits and stores the data.
Certain examples have other features that are one of in addition to and in lieu of the features illustrated in the above-referenced figures. These and other features are detailed below with reference to the above-referenced figures.